Answer: a^2 pi + 2ab
Step-by-step explanation:
Since the figure is composed of a rectangle and two semicircles, we can calculate the area of the rectangle and the semicircles separately.
The two semicircles together make up the circle. 2a is given as the diameter of the circle, so therefore, the radius of the circle is a.
The area of a circle is pi*radius^2 = pi*a^2 = a^2 pi.
The area of a rectangle is the length * width, which is 2a*b in this case = 2ab
Therefore, the total area is a^2 pi + 2ab.
